Nanoscale Disorder in CaCu3Ti4O12: A New Route to the Enhanced Dielectric Response

Y. Zhu,1,* J. C. Zheng,1 L. Wu,1 A. I. Frenkel,2 J. Hanson,1 P. Northrup,1 and W. Ku1

1Brookhaven National Laboratory, Upton, New York 11973, USA2Yeshiva University, New York, New York 10016, USA(Received 23 March 2007; published 18 July 2007)

Significant nanoscale disorder of Cu and Ca atomic substitution is observed in CaCu3Ti4O12, based onour integrated study using quantitative electron diffraction and extended x-ray absorption fine structure.Unambiguous identification of this previously omitted disorder is made possible by the unique sensitivityof these probes to valence-electron distribution and short-range order. Furthermore, first-principles-basedtheoretical analysis indicates that the Ca-site Cu atoms possess partially filled degenerate eg states,suggesting significant boost of dielectric response from additional low-energy electronic contributions.Our study points to a new route of enhancing dielectric response in transitional metal oxides by exploitingthe strong electronic correlation beyond classical static pictures.

DOI: 10.1103/PhysRevLett.99.037602 PACS numbers: 77.84.�s, 61.14.Lj, 71.20.�b, 78.70.Dm

The recent discovery of the prodigiously high dielectricconstant (� 105) of cubic CaCu3Ti4O12 (CCTO), the high-est ever measured in nonferroelectrics over a wide range oftemperature and frequency, attracted much attention [1–11]. Density functional theory (DFT) calculations based onthe ideal stoichiometric single crystal suggest that thematerial can only have an intrinsic dielectric constantfour orders of magnitude less than that observed experi-mentally [7]. After an exhaustive search for its intrinsicmechanism, attention was then shifted to defects that formthe ‘‘internal barrier layer capacitance’’ (IBLC) respon-sible for this anomalous behavior. Various morphologicalmodels were proposed [8]. The puzzling aspect is that thelong-expected twin boundaries in the system acting as theIBLC were never truly observed [10]. Furthermore, thetype and density of the defects are very different in singlecrystals, bulk ceramics, and thin films of CCTO [4], yet allexhibit similar dielectric behavior [10]. Clearly, there is ageneral interest as well as an urgent need to understand theorigin of the unusual dielectric property in CCTO. Theunderstanding can lead the exploration for the next gen-eration of high-dielectric materials.

In this Letter, we report our study of nanoscale disorderin single crystals of CCTO using unique techniques that aresensitive to local structural disorder. We reveal that there isconsiderable substitutional disorder at the Ca=Cu sites inthe system that was not observed by using volume-averaged scattering probes. We demonstrate that the en-hanced electronic dielectric response in CCTO can beattributed to the change of local electronic structure asso-ciated with Cu substitution of Ca.

CCTO has a cubic cell that is 2� 2� 2 times the size ofthe perovskite subcell ABO3, with Ca=Cu at the A sites andTi at the B sites. Because of the fairly large tilt of the TiO6

octahedra, 34 of the A atoms (i.e., the Cu atoms, hereafter

denoted as an A00 site with an mmm symmetry) are coor-dinated with four oxygen atoms forming a square with a Cuatom at the center. The remaining A atoms, Ca (A0 site with

a m-3 symmetry), have a bcc arrangement, and each issurrounded by a 12-oxygen icosahedral environment.

We investigated the same single crystals that werestudied previously by neutron scattering and optical con-ductivity [2]. The recent development of quantitative elec-tron diffraction (QED) [12–14] allows us to determinevalence electronic density by accurate measurement oflow-order structure factors due to the high sensitivity ofsmall-angle-scattered incident electrons to atomic ionicityand to the distribution of valence electrons that bond atomstogether. CCTO has several short scattering vectors be-cause of its relatively large cell dimension; hence, we cantake advantage of the QED technique, the paralleling re-cording of dark-field images (PARODI) method that wedeveloped recently to study valence-electron distributionin crystals with a large unit cell [15,16]. Although PARODIis more technically demanding than conventional conver-gent beam electron diffraction, it is more suitable to studycrystals with a large unit cell using small convergentangles.

The structure factors of low-order reflections were mea-sured using a 300 kV field-emission microscope with a postcolumn energy filter, and compared with first-principles-based DFT calculations. Starting with the structure factorsof free atoms, we simulate the diffraction patterns usingdynamic diffraction theory and compare them with theexperiment via a refinement procedure until a good agree-ment is reached. These experimental structure factors aremodel independent. Figures 1(a) and 1(b) are an exampleof structure factor measurement of CCTO using QED withthe comparison of experiment and calculation [Fig. 1(c)].We concentrate on the six innermost reflections (110, 200,211, 220, 400, and 422) that are most sensitive to thecharge and orbital electrons, but negligibly influenced bythe precision of atomic positions and thermal parameters.For reflections further out in reciprocal space, synchrotronx-ray diffraction (XRD) was used. The electron and x-raydata sets were combined, providing experimental measure-

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ments of 58 independent structure factors, and then con-verted to x-ray structure factors, which are the Fouriercomponents of charge density. Inverse Fourier transformand multipole refinement [17] of the data yield 3D charge-density distribution.

Figure 2(a) is the resulting experimental density map ofCCTO showing bonding valence states in the (001) plane,along with that calculated by DFT [Fig. 2(b)] within theLDA�U approximation. The magnetically active andorbital-ordered Cu-d states exhibit a well-defined t2g sym-metry [pointing toward the (110) directions], and formantibonds with neighboring O-p states, in good agreementwith calculations. Surprisingly, the states at A0 sites that aresupposed to be occupied by Ca also show orbital anisot-ropy with weak eg symmetry in Fig. 2(a), in clear contrastto the spherical density profile of Ca2� obtained from thetheoretical density map [Fig. 2(b)]. Since Cu atoms are theonly ones that have open d shell in this system, thisimmediately points to a considerable amount of Cu sub-stitution of Ca atoms. Similarly, the structure factors de-termined experimentally at 300 and 90 K are overall ingood agreement with DFT calculations, except those of thethree innermost reflections that are sensitive to the bondingelectrons, which show significant deviation from the cal-culations. Nevertheless, when A-site (Ca and Cu) disorder,as we reported previously [10], was taken into account,the deviation in refinement fell by a factor of 6. Thissuggests that the stoichiometrically ordered structure ofCCTO used in our DFT calculations is inadequate for

describing the electronic structure, particularly, the dielec-tric response.

To further explore local disorder, we conducted an ex-tended x-ray absorption fine structure (EXAFS) study thatis sensitive to local structure around selected atomic spe-cies and thus can provide unbiased information aboutshort-range order. The experiments were carried out atNSLS beam lines X11A for Ti and Cu and X15B for Ca,and all edges were analyzed concurrently using theUWXAFS package [18] that allows us to fit theoreticallycalculated EXAFS signals (using the FEFF6 program [19])to all three absorbing elements’ data. Because of the mul-tiple constraints imposed on the heterometallic bonds dur-ing their analysis from either edge, the total number ofadjustable variables (18) was much smaller than the num-ber of relevant independent data points (43). Figure 3shows the experimental EXAFS data, superimposed ontheir theoretical fits. Among several structural parametersvaried in the fits (e.g., metal-oxygen and metal-metal bondlengths and their disorders), the coordination numbers ofbonds between A-site atoms (Cu, Ca) are particularlyimportant for quantifying the short-range order in thissystem. Unexpectedly, the Cu-Ca and Ca-Cu coordinationnumbers N that varied independently in the fits were foundto be 3:2� 0:8 and 2:4� 1:6, respectively, i.e., outside theranges corresponding to the stoichiometric structure: 1:5<NCu-Ca < 2 and 4:5<NCa-Cu < 6. Each result indepen-dently points to the presence of a locally Ca-rich phaseCaCu1�xTiO3, where x > 0:25, suggesting the presence oflocal compositional disorder. Since XRD shows that theoverall sample composition (x � 0:25) is preserved, ourresults unambiguously point to the coexistence of non-

(a) (b)

-1.6

0.3

Cu

O

Ca

CuCu

Cu

O

Ca

Cu Cu

A’site

A”site

e/Å3

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-1.6

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Cu

O

Ca

CuCu

Cu

O

Ca

CuCu

Cu

O

Ca

Cu Cu

Cu

O

Ca

Cu Cu

A’siteA’site

A”siteA”site

e/Å3

FIG. 2 (color). The bonding-electron distribution of CCTO in(001) basal plane containing Cu, Ca, and O atoms.(a) Experimental observation extracted from structure factormeasurements using combined electron and x-ray diffractiondata (i.e., the static deformation electron density map usingneutral atoms as a reference). (b) DFT calculation based onthe ideal crystal structure. The color legend indicates the mag-nitude of the charge, and the contour plot has an interval of0:1 e= �A3. The orbital-ordered Cu 3d states of xy symmetry areclearly visible, as well as its antibonding with O 2p states. Notethe significant difference near the A0 sites (circled by solid line)between (a) and (b), where an anisotropic density pattern of egelectrons is observed only experimentally, suggesting somedegree of disorder with Cu replacing Ca in real material.

(a)

(b)-400 -200 000 200 400

inte

nsity

200 004002--400 000(c)

(a)

(b)-400 -200 000 200 400

(a)

(b)-400 -200 000 200 400

inte

nsity

200 004002--400 000(c)

inte

nsity

200 004002--400 000000(c)

FIG. 1 (color). Measurement of low-order structure factorsusing quantitative electron diffraction. (a) An experimentalPARODI pattern of CCTO recorded on a 20 bit imaging plateshowing the h00 systematical row of the 000, �200, and �400reflections at room temperature. (b) Calculated pattern using thedynamic Bloch-wave approach. (c) Line scans of the intensityoscillation from (a) as open circles are compared with calcula-tions in (b) as solid lines. The best fits of the experimental dataand calculations yield structure factors of low-order reflectionsthat are the foundation of our bonding-electron measurement, aswell as revealing the disordered structure in the system.

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stoichiometric nanophases with x < 0:25. Presence of localstructural disorder is also independently supported by theresults of Ti-A and Cu-A bond length measurements thatwere found to be shorter for A � Ca (3:18� 0:02 �A and3:68� 0:02 �A, respectively) than for A � Cu (3:22�0:01 �A and 3:74� 0:02 �A, respectively). While such de-viations of the local structure inferred from EXAFS fromthe average structure, ascertained by XRD, may merelyindicate local bond buckling of the actual structure aroundthe average lattice [20] and do not necessarily require localdeviations from stoichiometry, the sign of the bond lengthmismatch is not consistent with a single-phase substitu-tional alloy since the ionic size of Cu (0.65 A) is smallerthan Ca (0.99 A). Such difference is expected, however, ina system separated into several, disjoint, off-stoichiometricphases. The fact that the Cu environment is more stronglydisordered than that of Ca means that Cu-rich regions havelower dimensionality than the Ca-rich ones.

We note that the local disorder in CCTO measured byEXAFS has not been revealed by previous studies of XRD[3], similar to other analogous systems [21–23].Observation of local disorder in CCTO is not straightfor-ward because in its I3m structure the substitution of Cu atCa sites, or vice versa, results in changes only in the

intensity of the ooe class of reflections (o and e refer toodd and even numbers, respectively) but does not result inany change to the eee reflections. Consequently, the nor-mal least squares refinement parameters for the entire dataset are not very sensitive to the substitution and the changeof the goodness of fit with and without 5% substitution isnegligibly small. Nevertheless, our finding agrees with therecent observations, from atomic-pair distribution functionanalysis, that in CCTO there is unusual temperature de-pendence of the displacement and significant bondingstrain of Ca and Cu under a stoichiometric atomic environ-ment [11]. As discussed above, our multiple-edge study ofEXAFS further suggests that the Cu-rich regions are moredisordered, or have reduced dimensionality, than the Ca-rich ones. This is consistent with our DFT-basedformation-energy calculations that the Ca-rich phase isenergetically favorable while the Cu-rich one is not, inagreement with our TEM observations. We found no evi-dence of enhanced values of Cu-O, Ti-O, or Ca-O bondlength disorder (compared to thermal disorder), thus rulingout measurable oxygen-atom disorder and, in turn, itspossible role in conductivity. Similar disordered nanoscalephases were previously observed with EXAFS [24,25].

The observed local disorder provides an interesting ‘‘ex-trinsic’’ feature that may account for the huge dielectricresponse of CCTO. As illustrated in Fig. 4, analysis of thelocal symmetry of low-energy electron orbitals shows thatwhile the t2g states of Cu at the ideal A00 site support theinsulating phase by splitting the degeneracy via orbitalordering (accompanied by tilting of the TiO6 octahedra),the eg states of Cu located at the Ca site (A0-site Cu) remaindegenerate within the local cubiclike symmetry, as evidentfrom our DFT calculation. Therefore, in the presence ofintersite d-d transition or on-site transition permitted byweak (e.g., phonon-assisting) symmetry breaking, a singu-larly large ‘‘metallic’’ dielectric response is expected nearthe A0-Cu sites. Since the insulating characteristics of thebulk material are only derived from the orbital ordering,significant enhancement of the dielectric response in thenearby insulating region can result from various ‘‘proxim-ity effects,’’ including their coupling to the A0-site-Custates as well as the disruption of their orbital orderingthat leads to low-energy excitons (e.g., reduced localcharge gap and the so-called ‘‘orbiton’’ excitations in thegap). In a simplest picture, the local dielectric responsewould feature singularly large value centered at eachA0-site Cu with a smooth decay in space. Formulated in acontinuous model (with zero-dimension conducting re-gions), the bulk dielectric function "�1

tot �1V

R"�1�x�d3x

could reach very large values, provided that only a verysmall portion of the volume is far from any of the A0-siteCu, as suggested by our EXAFS data, to possess smallenough local dielectric response that dominates theintegral.

The existence of large volume fraction of high-dielectricinsulating regions in this picture resolves a dilemma of

0 2 4 6 80

1

2

3

4

Ca edge

Ti edge

FT

Mag

nitu

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a.u.

)

r, Å

Cu edge

0 2 4 6 80

1

2

3

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Ca edge

Ti edge

FT

Mag

nitu

de (

a.u.

)

r, Å

Cu edge

FIG. 3 (color). The Ti, Cu, and Ca K edges of the EXAFS data(black) and their theoretical fits (red). Some data and fits arerescaled and shifted vertically for clarity. The k ranges forFourier transforms (uncorrected for the photoelectron phaseshifts) for Cu, Ti, and Ca were from 2 to 15, 13, or 10 �A�1,respectively. The first peak in the Ti EXAFS data is due to thefirst nearest neighbor Ti-O bonds. The second peak in the Ti datais due to the mixture of Ti-Ca and Ti-Cu contributions. Thesimilar range of distances in Cu is contributed by Cu-O, Cu-Ti,Cu-Ca, and Cu-Cu paths. For better contrast of Cu-Ca and Cu-Cu contributions, we weighted the Cu data with k3 in theanalysis, and all others with k2. For Ca atoms, the relativelylow value of kmax � 10 �A�1 does not allow the visual resolutionof four contributions (Ca-O, Ca-Ti, Ca-Ca, and Ca-Cu) to the rrange between 1 and 4 �A corresponding to the broad first peak inCa EXAFS. These contributions were accounted for in the dataanalysis.

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several proposed conventional extrinsic models [8]; i.e.,only a very small fraction (� 10�3) of insulating regions isallowed, yet the transport has to be totally impeded withoutthe surface-blocking layers. Furthermore, the crucial roleof disorder in our picture provides a natural resolution tothe well-known puzzle of why CdCu3Ti4O12 has a verydifferent dielectric response from that of CCTO despitetheir almost identical electronic structures and similar sizesof Cd and Ca: the nature of the intrinsic disorder could bevery different in the two materials. In fact, our viewpointon the importance of disorder is indirectly supported byrecent experiments [26,27].

In summary, our integrated study using QED, XRD,EXAFS, and first-principles theory evidently reveals theexistence of nanoscale disorder of Cu=Ca and suggests itsremarkable effects on the dielectric properties of CCTO.Specifically, the higher local symmetry of the A0 siterecovers the orbital freedom of Cu when substituting Ca,which, in turn, can induce a metalliclike polarizability inthe surrounding insulating regions, hence yielding drasti-cally enhanced dynamical electronic dielectric response.We propose that such significant enhancement of dielectricresponse due to disorder-induced recovery of orbital de-generacy is a genuine feature in orbital-ordered stronglycorrelated electron systems. This microscopic mechanismof boosting the dielectric response opens a door to thedesign of new functional materials in strongly correlatedinsulators, such as manganites, by utilizing their orbitalfreedom via tailoring atomic substitution and disorder.

We thank S. Wakimoto for providing the single crystalsand M. H. Cohen, D. Vanderbilt, and J. Tafto for stimulat-ing discussions. Work at Brookhaven was supported by theU.S. Department of Energy, Office of Basic EnergyScience, under Contracts No. DE-AC02-98CH10886,No. DE-FG02-05ER36184, and DOE-CMSN.

*Corresponding author.zhu@bnl.gov

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(2006).

eg

t2g

ag

eg’

eg

DOS

EF

(b)

t2g

eg

Cu at A’’ site Cu at A’ site

(a)E

Cu3d

ag

eg’

eg

Cu at A’’ site Cu at A’ site

FIG. 4 (color). Tendency towards degeneracy in disordered Cu3d in CCTO (A0A003Ti4O12). Left: Cu at A00 site (mmm) withA0 � Ca. Right: Cu substituting at one of the two A0 sites (m-3)with A00 � Cu in the 40-atom unit cell. (a) Symmetry analysis ofdegeneracy of local d electronic states of Cu. (b) Partial densityof spin-minority states (states per electronvolt cell spin) of Cubased on DFT (LSDA�U, U � 4 eV) calculations of periodicsystems. The Fermi level lies at zero energy. In the ideal CCTO(left), the orbital ordering associated with the O-octahedral tiltbreaks the degeneracy of t2g, while in the disordered region(right) the cubiclike symmetry at the A0 site retains the egdegeneracy, and thus exhibits metalliclike behavior and enablesa large local dielectric response.

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